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 A229723 Expansion of psi(q) * chi(-q^3) * phi(-q^6) in powers of q where phi(), psi(), chi() are Ramanujan theta functions. 3
 1, 1, 0, 0, -1, 0, -2, -2, 0, -2, 2, 0, 0, 0, 0, 4, -1, 0, 0, 0, 0, 0, 2, 0, 2, 3, 0, 0, -2, 0, 0, -2, 0, -4, 0, 0, 2, 0, 0, 0, -2, 0, -4, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -2, -4, 0, 0, 2, 0, 4, 0, 0, 4, -1, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, -2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Michael Somos, Introduction to Ramanujan theta functions Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion eta(q^2)^2 * eta(q^3) * eta(q^6) / (eta(q) * eta(q^12)) in powers of q. Euler transform of period 12 sequence [ 1, -1, 0, -1, 1, -3, 1, -1, 0, -1, 1, -2, ...]. G.f. is a period 1 Fourier series which satisfies f(-1 / (288 t)) = 13824^(1/2) (t / i) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A128583. a(3*n + 2) = 0. EXAMPLE G.f. = 1 + q - q^4 - 2*q^6 - 2*q^7 - 2*q^9 + 2*q^10 + 4*q^15 - q^16 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ QPochhammer[ q^3, q^6] EllipticTheta[ 4, 0, q^6] EllipticTheta[ 2, 0, q^(1/2)] / (2 q^(1/8)), {q, 0, n}]; a[ n_] := SeriesCoefficient[ QPochhammer[ q^2]^2 QPochhammer[ q^3] QPochhammer[ q^6]/ (QPochhammer[ q] QPochhammer[ q^12]), {q, 0, n}]; PROG (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^3 + A) * eta(x^6 + A) / (eta(x + A) * eta(x^12 + A)), n))}; CROSSREFS Cf. A128583. Sequence in context: A214667 A214665 A352557 * A258040 A215879 A114700 Adjacent sequences: A229720 A229721 A229722 * A229724 A229725 A229726 KEYWORD sign AUTHOR Michael Somos, Sep 27 2013 STATUS approved

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Last modified May 31 12:12 EDT 2023. Contains 363066 sequences. (Running on oeis4.)